When Little Stevie boldly declares, "I ain't gonna play Sun City," it might be a good answer to the question. In 1984, artist Steven Van Zandt gathered the most prominent of musicians in music to protest South Africa's use of apartheid (mentioned above) in refusing to play at the resort of Sun City. This helps to bring to light how economic sanctions and boycotts can be used as a call to action in order to ensure that human rights is something that is universally accepted. Nations have always felt that being able to use commerce and material means to help advocate policies that benefit citizens can be quite useful. It is much more cost effective than declaring a war or shunning a nation from its discourse. There are some who suggest that using such economic means will be essential in getting nations like China to respect human rights in a more significant manner. For a nation that does not demonstrate a great deal of acceptance and embracing the notion of human rights for all of its citizens, some argue that the only language that can be heard is that of economic rights and the ability to impact the Chinese economy. In a more topical manner, economic means has been used with nations to ensure that a greater emphasis on fighting terrorism is something that is universally shared. One of the most prominent moves that America made in the months that followed the attacks of September 11 was to forgive the outstanding (and quite significant) debt that Pakistan owed the United States in exchange for being able to use the nation as a launching ground for its endeavors in Afghanistan and to ensure that the tribal regions would be swept for those deemed as enemies of the United States.
I think that you could say that there are two ways in which this has happened -- one that is punitive and one that is more of an inducement.
As far as the inducements go, many countries (notably those in the West) have given aid to countries in an attempt to get them to respect human rights. They have, for example, tried to help countries set up systems of law that will be more supportive of human rights.
On the more punitive side, countries sometimes use economic sanctions against countries that do not respect human rights. For example, there were many countries that refused to do business to some extent or other with South Africa back when it practiced apartheid.
Some countries have tried to encourage other countries to have greater respect and protection of human rights by several economic measures. Such action may be direct prohibition of economic trade and assistance to countries in which governments commit actions that are considered to be gross violation of human rights. Countries may may also take limited economic measures such as prohibiting import of goods that have been manufactured in gross violation of human rights, such as employment of child labour.